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%I #16 Sep 08 2022 08:46:15
%S 0,-1,8,-16,30,-45,66,-88,116,-145,180,-216,258,-301,350,-400,456,
%T -513,576,-640,710,-781,858,-936,1020,-1105,1196,-1288,1386,-1485,
%U 1590,-1696,1808,-1921,2040,-2160,2286,-2413,2546,-2680,2820,-2961,3108,-3256,3410
%N Alternating sum of 9-gonal (or nonagonal) numbers.
%H G. C. Greubel, <a href="/A266086/b266086.txt">Table of n, a(n) for n = 0..5000</a>
%H OEIS Wiki, <a href="http://oeis.org/wiki/Figurate_numbers">Figurate numbers</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/NonagonalNumber.html">Nonagonal Number</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-2,0,2,1).
%F G.f.: -x*(1 - 6*x)/((1 - x)*(1 + x)^3).
%F a(n) = ((14*n^2 + 4*n - 5)*(-1)^n + 5)/8.
%F a(n) = Sum_{k = 0..n} (-1)^k*A001106(k).
%F Lim_{n -> infinity} a(n + 1)/a(n) = -1.
%t Table[((14 n^2 + 4 n - 5) (-1)^n + 5)/8, {n, 0, 44}]
%t CoefficientList[Series[(x - 6 x^2)/(x^4 + 2 x^3 - 2 x - 1), {x, 0, 50}], x] (* _Vincenzo Librandi_, Dec 21 2015 *)
%o (Magma) [(14*(-1)^n*n^2 + 4*(-1)^n*n - 5*(-1)^n + 5)/8: n in [0..50]]; // _Vincenzo Librandi_, Dec 21 2015
%o (PARI) x='x+O('x^100); concat(0, Vec(-x*(1-6*x)/((1-x)*(1+x)^3))) \\ _Altug Alkan_, Dec 21 2015
%Y Cf. A001106, A006578, A007584, A035608, A083392, A089594.
%K sign,easy
%O 0,3
%A _Ilya Gutkovskiy_, Dec 21 2015
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